The Longest Path Problem on Permutation Graphs

نویسندگان

  • Ruei-Yuan Chang
  • Cheng-Hsien Hsu
  • Sheng-Lung Peng
چکیده

The longest path problem on graph G is a classic problem which is to find a simple path such that the number of vertices of the path is maximum among all possible paths of G. In this paper, we show that the longest path problem can be solved in linear time on permutation graphs.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Linear structure of bipartite permutation graphs and the longest path problem

The class of bipartite permutation graphs is the intersection of two well known graph classes: bipartite graphs and permutation graphs. A complete bipartite decomposition of a bipartite permutation graph is proposed in this note. The decomposition gives a linear structure of bipartite permutation graphs, and it can be obtained in O(n) time, where n is the number of vertices. As an application o...

متن کامل

Polynomial-time algorithms for the Longest Induced Path and Induced Disjoint Paths problems on graphs of bounded mim-widthh

We give the first polynomial-time algorithms on graphs of bounded maximum induced matching width (mim-width) for problems that are not locally checkable. In particular, we give nO(w)-time algorithms on graphs of mim-width at most w, when given a decomposition, for the following problems: Longest Induced Path, Induced Disjoint Paths and H-Induced Topological Minor for fixed H. Our results imply ...

متن کامل

Polynomial-Time Algorithms for the Longest Induced Path and Induced Disjoint Paths Problems on Graphs of Bounded Mim-Width

We give the first polynomial-time algorithms on graphs of bounded maximum induced matching width (mim-width) for problems that are not locally checkable. In particular, we give nO(w)-time algorithms on graphs of mim-width at most w, when given a decomposition, for the following problems: Longest Induced Path, Induced Disjoint Paths and H-Induced Topological Minor for fixed H. Our results imply ...

متن کامل

NC Coloring Algorithms for Permutation Graphs

We show that the problem of coloring a permutation graph of size n can be solved in O(logn logk) time using O(kn2 / logk log2n) processors on the CREW PRAM model of computation, where 1 < k < n. We estimate the parameter k on random permutation graphs and show that the coloring problem can be solved in O(logn loglogn) time in the average-case on the CREW PRAM model of computation with O(n2) pro...

متن کامل

Longest Path Problems on Ptolemaic Graphs

SUMMARY Longest path problem is a problem for finding a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, there are few known graph classes such that the longest path problem can be solved efficiently. Polynomial time algorithms for finding a longest cycle and a longest path in a Ptolemaic graph are pr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012